Then inside this definition as you can see we obsereved,

on one side transformation of the partial indicators.

We see also a parameter beta that we will explain later in the course.

And we will see also what we call w1, w2, wn, which are the weights.

And then let us go a bit to the slide number three,

where we would like to point out basically that a composite indicator

is just a weighted average of the transform indicators of order beta.

This is just an composite indicator, a weighted average in terms of that.

So in principle as you might see all these slides are tending or

are showing that in the way we are looking at composite indicators.

We have only a question or name of order individuals or

order in societies, or order in countries, good.

What are the reasons for their transformation, you might ask

about this transformation we find this capital I in the expression.

There are mainly two reason why which is to make this transformation.

The first reason is that variable usually are measure in different units.

And at some point, of course, to make this composite indicator

inaggregate, we need to make homogeneous all these measurements.

Second reason why we have this transformation,

is the fact that there might be outliers, there might be missing values.

And all that are going to somehow disturb our analysis.

And this is why somehow we decide to make these transformations.

Okay, if we go the next slide, you will see fairly nice

definition of what is preferred or what is indifferent between two countries.

We say country i is preferred to country k, if the value that takes partial

indicator for country i is larger than the values this indicator takes for country k.

On the other side, we will say both countries are indifferent whether

the value that the indicators i takes for country.

Then this indicator or this partial indicator takes for

country i is equal to the value that this pattern indicator takes for country k.

So what this basically, let us go to the next slide then,

we will see there basically what is the problem of defining of

elaborating a composite indicator.

The problem is just basically to chose the weights,

to choose the transformation and to chose the beta.

And then once we have done this, try to order the results in terms of individuals,

in terms of countries or whatever it is that we are trying to measure.

So if you remember, we said before that the principles we were going to establish

in terms of the composite indicators, well for a good, or we said good criterias.

For composite indicators, we're going to depend on the target, we wanted to aim to.

In this case, our target is how to rank?

How to rank countries or individuals according to

the value these composite indicators are taking?

Okay, of course, we can pass now to the next slide.

Of course, what we can realize is that if we are trying to order individuals or

we are trying to order countries, we have a basic problem, right?